def test_odeint_required_dtypes(self):
with self.assertRaisesRegexp(TypeError,
'`y0` must have a floating point'):
odes.odeint(self.func, math_ops.cast(self.y0, dtypes.int32),
[0, 1])
with self.assertRaisesRegexp(TypeError,
'`t` must have a floating point'):
odes.odeint(self.func, self.y0, math_ops.cast([0, 1],
dtypes.int32))
def test_odeint_5th_order_accuracy(self):
t = [0, 20]
kwargs = dict(
full_output=True, method='dopri5', options=dict(max_num_steps=2000))
with self.test_session() as sess:
_, info_0 = sess.run(
odes.odeint(self.func, self.y0, t, rtol=0, atol=1e-6, **kwargs))
_, info_1 = sess.run(
odes.odeint(self.func, self.y0, t, rtol=0, atol=1e-9, **kwargs))
self.assertAllClose(
info_0['integrate_points'].size * 1000**0.2,
float(info_1['integrate_points'].size),
rtol=0.01)
def test_odeint_different_times(self):
# integrate steps should be independent of interpolation times
times0 = np.linspace(0, 10, num=11, dtype=float)
times1 = np.linspace(0, 10, num=101, dtype=float)
with self.test_session() as sess:
y_solved_0, info_0 = sess.run(
odes.odeint(self.func, self.y0, times0, full_output=True))
y_solved_1, info_1 = sess.run(
odes.odeint(self.func, self.y0, times1, full_output=True))
self.assertAllClose(y_solved_0, y_solved_1[::10])
self.assertEqual(info_0['num_func_evals'], info_1['num_func_evals'])
self.assertAllEqual(info_0['integrate_points'], info_1['integrate_points'])
self.assertAllEqual(info_0['error_ratio'], info_1['error_ratio'])
def test_odeint_runtime_errors(self):
with self.assertRaisesRegexp(ValueError, 'cannot supply `options` without'):
odes.odeint(self.func, self.y0, [0, 1], options={'first_step': 1.0})
y = odes.odeint(
self.func,
self.y0, [0, 1],
method='dopri5',
options={'max_num_steps': 0})
with self.test_session() as sess:
with self.assertRaisesRegexp(errors_impl.InvalidArgumentError,
'max_num_steps'):
sess.run(y)
y = odes.odeint(self.func, self.y0, [1, 0])
with self.test_session() as sess:
with self.assertRaisesRegexp(errors_impl.InvalidArgumentError,
'monotonic increasing'):
sess.run(y)
def test_odeint_riccati(self):
# The Ricatti equation is:
# dy / dt = (y - t) ** 2 + 1.0, y(0) = 0.5.
# Its analytical solution is y = 1.0 / (2.0 - t) + t.
func = lambda t, y: (y - t)**2 + 1.0
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, np.float64(0.5), t)
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = 1.0 / (2.0 - t) + t
self.assertAllClose(y_true, y_solved)
def test_odeint_riccati(self):
# The Ricatti equation is:
# dy / dt = (y - t) ** 2 + 1.0, y(0) = 0.5.
# Its analytical solution is y = 1.0 / (2.0 - t) + t.
func = lambda t, y: (y - t)**2 + 1.0
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, np.float64(0.5), t)
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = 1.0 / (2.0 - t) + t
self.assertAllClose(y_true, y_solved)
def test_odeint_complex(self):
# Test a complex, linear ODE:
# dy / dt = k * y, y(0) = 1.0.
# Its analytical solution is y = exp(k * t).
k = 1j - 0.1
func = lambda y, t: k * y
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, 1.0 + 0.0j, t)
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = np.exp(k * t)
self.assertAllClose(y_true, y_solved)
def test_odeint_higher_rank(self):
func = lambda y, t: y
y0 = constant_op.constant(1.0, dtype=dtypes.float64)
t = np.linspace(0.0, 1.0, 11)
for shape in [(), (1, ), (1, 1)]:
expected_shape = (len(t), ) + shape
y_solved = odes.odeint(func, array_ops.reshape(y0, shape), t)
self.assertEqual(y_solved.get_shape(),
tensor_shape.TensorShape(expected_shape))
with self.test_session() as sess:
y_solved = sess.run(y_solved)
self.assertEquals(y_solved.shape, expected_shape)
def test_odeint_complex(self):
# Test a complex, linear ODE:
# dy / dt = k * y, y(0) = 1.0.
# Its analytical solution is y = exp(k * t).
k = 1j - 0.1
func = lambda y, t: k * y
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, 1.0 + 0.0j, t)
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = np.exp(k * t)
self.assertAllClose(y_true, y_solved)
def test_odeint_higher_rank(self):
func = lambda y, t: y
y0 = constant_op.constant(1.0, dtype=dtypes.float64)
t = np.linspace(0.0, 1.0, 11)
for shape in [(), (1,), (1, 1)]:
expected_shape = (len(t),) + shape
y_solved = odes.odeint(func, array_ops.reshape(y0, shape), t)
self.assertEqual(y_solved.get_shape(),
tensor_shape.TensorShape(expected_shape))
with self.test_session() as sess:
y_solved = sess.run(y_solved)
self.assertEquals(y_solved.shape, expected_shape)
def test_odeint_exp(self):
# Test odeint by an exponential function:
# dy / dt = y, y(0) = 1.0.
# Its analytical solution is y = exp(t).
func = lambda y, t: y
y0 = constant_op.constant(1.0, dtype=dtypes.float64)
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, y0, t)
self.assertIn('odeint', y_solved.name)
self.assertEqual(y_solved.get_shape(), tensor_shape.TensorShape([11]))
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = np.exp(t)
self.assertAllClose(y_true, y_solved)
def test_odeint_exp(self):
# Test odeint by an exponential function:
# dy / dt = y, y(0) = 1.0.
# Its analytical solution is y = exp(t).
func = lambda y, t: y
y0 = constant_op.constant(1.0, dtype=dtypes.float64)
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, y0, t)
self.assertIn('odeint', y_solved.name)
self.assertEqual(y_solved.get_shape(), tensor_shape.TensorShape([11]))
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = np.exp(t)
self.assertAllClose(y_true, y_solved)
def test_odeint_all_dtypes(self):
func = lambda y, t: y
t = np.linspace(0.0, 1.0, 11)
for y0_dtype in [
dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
]:
for t_dtype in [dtypes.float32, dtypes.float64]:
y0 = math_ops.cast(1.0, y0_dtype)
y_solved = odes.odeint(func, y0, math_ops.cast(t, t_dtype))
with self.test_session() as sess:
y_solved = sess.run(y_solved)
expected = np.asarray(np.exp(t))
self.assertAllClose(y_solved, expected, rtol=1e-5)
self.assertEqual(dtypes.as_dtype(y_solved.dtype), y0_dtype)
def test_odeint_2d_linear(self):
# Solve the 2D linear differential equation:
# dy1 / dt = 3.0 * y1 + 4.0 * y2,
# dy2 / dt = -4.0 * y1 + 3.0 * y2,
# y1(0) = 0.0,
# y2(0) = 1.0.
# Its analytical solution is
# y1 = sin(4.0 * t) * exp(3.0 * t),
# y2 = cos(4.0 * t) * exp(3.0 * t).
matrix = constant_op.constant([[3.0, 4.0], [-4.0, 3.0]],
dtype=dtypes.float64)
func = lambda y, t: math_ops.matmul(matrix, y)
y0 = constant_op.constant([[0.0], [1.0]], dtype=dtypes.float64)
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, y0, t)
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = np.zeros((len(t), 2, 1))
y_true[:, 0, 0] = np.sin(4.0 * t) * np.exp(3.0 * t)
y_true[:, 1, 0] = np.cos(4.0 * t) * np.exp(3.0 * t)
self.assertAllClose(y_true, y_solved, atol=1e-5)
def test_odeint_2d_linear(self):
# Solve the 2D linear differential equation:
# dy1 / dt = 3.0 * y1 + 4.0 * y2,
# dy2 / dt = -4.0 * y1 + 3.0 * y2,
# y1(0) = 0.0,
# y2(0) = 1.0.
# Its analytical solution is
# y1 = sin(4.0 * t) * exp(3.0 * t),
# y2 = cos(4.0 * t) * exp(3.0 * t).
matrix = constant_op.constant(
[[3.0, 4.0], [-4.0, 3.0]], dtype=dtypes.float64)
func = lambda y, t: math_ops.matmul(matrix, y)
y0 = constant_op.constant([[0.0], [1.0]], dtype=dtypes.float64)
t = np.linspace(0.0, 1.0, 11)
y_solved = odes.odeint(func, y0, t)
with self.test_session() as sess:
y_solved = sess.run(y_solved)
y_true = np.zeros((len(t), 2, 1))
y_true[:, 0, 0] = np.sin(4.0 * t) * np.exp(3.0 * t)
y_true[:, 1, 0] = np.cos(4.0 * t) * np.exp(3.0 * t)
self.assertAllClose(y_true, y_solved, atol=1e-5)
def test_odeint_required_dtypes(self):
with self.assertRaisesRegexp(TypeError, '`y0` must have a floating point'):
odes.odeint(self.func, math_ops.cast(self.y0, dtypes.int32), [0, 1])
with self.assertRaisesRegexp(TypeError, '`t` must have a floating point'):
odes.odeint(self.func, self.y0, math_ops.cast([0, 1], dtypes.int32))
